Incidentally, I think it is a fascinating technique....I have never been able to use it in my work though....Thanks for the explanation! I'll stick with the high level concept for now, hopefully we won't have to calculate any eigenvalues...
@brian.field is the eigenvalue of PCA the same thing explaines the curviture and shape of the model? I was trying to associate canonical table of data from my design and experiment class to PCAs...prob not necessary...The components are mathematical/theoretical constructs....the components would NOT be the 2 year and the 30 year if you were to use PCA in your example. PCA in a problem with only 2 independent variables would be inappropriate. I forget the details, so some of my statements may be off slightly, but if I remember correctly, PCA is appropriate for high dimensional problems. It is a dimension reduction technique used in multivariate statistics. The PCA approach identifies eigenvalues/eigenvectors that "explain" the behavior of the data. Eigenvalues/vectors are, by definition, perpendicular, or in other words, uncorrelated, i.e., their dot products are 0. Say you have 10 eigenvalues....the first 4 of them might explain 95% of the behavior in the data, so you could effectively utilize the 4 principal components associated with the 4 eigenvalues rather than using all 10 since last 6 appear unimportant as they explain only 5% of the behavior. So, you will have reduced the dimensionality down from 10 to 4.